Multiple Choice
Factor completely.
7. Factoring
Factoring Trinomials of the Form ax² + bx + c
Multiple Choice
Factor the following polynomial
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Verified step by step guidance1
Identify the polynomial to factor: \(2x^{2} + 7xy + 3y^{2}\).
Look for two binomials of the form \((ax + by)(cx + dy)\) whose product gives the original polynomial.
Find two numbers that multiply to the product of the first and last coefficients (i.e., \(2 \times 3 = 6\)) and add up to the middle coefficient (7). These numbers are 6 and 1.
Rewrite the middle term \$7xy$ as \(6xy + 1xy\) to split the polynomial: \(2x^{2} + 6xy + 1xy + 3y^{2}\).
Group terms and factor each group: \((2x^{2} + 6xy) + (1xy + 3y^{2})\), then factor out the greatest common factor from each group to get \(2x(x + 3y) + y(x + 3y)\), and finally factor out the common binomial \((x + 3y)\) to get \((2x + y)(x + 3y)\).